7自由度机械臂操作空间matlab代码

以下是一个简单的7自由度机械臂操作空间的 MATLAB 代码示例：

% 机械臂参数
L1 = 1;
L2 = 1;
L3 = 1;
L4 = 1;
L5 = 1;
L6 = 1;
L7 = 1;

% 初始位置
theta1 = 0;
theta2 = 0;
theta3 = 0;
theta4 = 0;
theta5 = 0;
theta6 = 0;
theta7 = 0;

% 正运动学（计算末端位置）
T01 = DHparam(0, pi/2, 0, theta1);
T12 = DHparam(L1, 0, 0, theta2);
T23 = DHparam(L2, 0, 0, theta3);
T34 = DHparam(L3, 0, 0, theta4);
T45 = DHparam(L4, pi/2, 0, theta5);
T56 = DHparam(L5, -pi/2, 0, theta6);
T67 = DHparam(L6, 0, 0, theta7);
T7E = DHparam(L7, 0, 0, 0);
T0E = T01 * T12 * T23 * T34 * T45 * T56 * T67 * T7E;
P = T0E(1:3, 4); % 末端位置

% 逆运动学（计算关节角度）
% TODO: 实现逆运动学算法

% 末端运动学（在关节空间内随机运动）
while true
    % 生成随机目标点
    target = [rand(1)*2-1, rand(1)*2-1, rand(1)*2-1];
    
    % 计算当前位置
    T01 = DHparam(0, pi/2, 0, theta1);
    T12 = DHparam(L1, 0, 0, theta2);
    T23 = DHparam(L2, 0, 0, theta3);
    T34 = DHparam(L3, 0, 0, theta4);
    T45 = DHparam(L4, pi/2, 0, theta5);
    T56 = DHparam(L5, -pi/2, 0, theta6);
    T67 = DHparam(L6, 0, 0, theta7);
    T7E = DHparam(L7, 0, 0, 0);
    T0E = T01 * T12 * T23 * T34 * T45 * T56 * T67 * T7E;
    P = T0E(1:3, 4);
    
    % 计算目标位置与当前位置之间的向量
    error = target - P;
    
    % 计算雅可比矩阵
    J = jacobian(theta1, theta2, theta3, theta4, theta5, theta6, theta7);
    
    % 计算关节角速度
    dq = inv(J) * error';
    
    % 更新关节角度
    theta1 = theta1 + dq(1);
    theta2 = theta2 + dq(2);
    theta3 = theta3 + dq(3);
    theta4 = theta4 + dq(4);
    theta5 = theta5 + dq(5);
    theta6 = theta6 + dq(6);
    theta7 = theta7 + dq(7);
    
    % 绘制机械臂
    plot_robot(theta1, theta2, theta3, theta4, theta5, theta6, theta7);
    drawnow;
end

% DH参数计算函数
function T = DHparam(d, alpha, a, theta)
    T = [cos(theta), -sin(theta)*cos(alpha), sin(theta)*sin(alpha), a*cos(theta);
         sin(theta), cos(theta)*cos(alpha), -cos(theta)*sin(alpha), a*sin(theta);
         0, sin(alpha), cos(alpha), d;
         0, 0, 0, 1];
end

% 雅可比矩阵计算函数
function J = jacobian(theta1, theta2, theta3, theta4, theta5, theta6, theta7)
    L1 = 1;
    L2 = 1;
    L3 = 1;
    L4 = 1;
    L5 = 1;
    L6 = 1;
    L7 = 1;
    
    J = [L1*sin(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)+L1*cos(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)+L1*cos(theta1)*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)+L1*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7), L2*cos(theta1)*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)+L2*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)+L3*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)+L4*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)+L5*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)+L6*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)+L7*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7), -L2*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*cos(theta1)*cos(theta2)*sin(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L3*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L4*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L5*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L6*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L7*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7), -L2*cos(theta1)*sin(theta2)*sin(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*sin(theta1)*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L3*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L4*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L5*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L6*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L7*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7), L1*sin(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*cos(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*sin(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*cos(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L3*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L4*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L5*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L6*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L7*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7), -L1*cos(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*sin(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*cos(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*sin(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L3*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L4*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L5*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L6*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L7*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7), -L1*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*sin(theta2)*sin(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L2*sin(theta2)*sin(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L3*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L4*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L5*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L6*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L7*cos(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7), L1*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*cos(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*sin(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*cos(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L3*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L4*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L5*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L6*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L7*cos(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7), L1*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*sin(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L1*sin(theta1)*sin(theta2)*sin(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*cos(theta1)*sin(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*sin(theta1)*cos(theta2)*sin(theta3)*cos(theta4)*cos(theta5)*sin(theta6)*sin(theta7)-L2*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L3*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L4*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L5*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L6*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)-L7*sin(theta1)*sin(theta2)*cos(theta3)*sin(theta4)*sin(theta5)*cos(theta6)*sin(theta7)];
end

% 机械臂绘制函数
function plot_robot(theta1, theta2, theta3, theta4, theta5, theta6, theta7)
    L1 = 1;
    L2 = 1;
    L3 = 1;
    L4 = 1;
    L5 = 1;
    L6 = 1;
    L7 = 1;
    
    % 计算每个关节的位置
    P0 = [0, 0, 0];
    P1 = P0 + [L1*cos(theta1), L1*sin(theta1), 0];
    P2 = P1 + [L2*cos(theta1)*cos(theta2), L2*sin(theta1)*cos(theta2), L2*sin(theta2)];
    P3 = P2 + [L3*cos(theta1)*cos(theta2)*cos(theta3)-L3*sin(theta1)*sin(theta3), L3*sin(theta1)*cos(theta2)*cos(theta3)+L3*cos(theta1)*sin(theta3), L2+L3*cos(theta2)*sin(theta3)];
    P4 = P3 + [L4*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)-L4*sin(theta1)*sin(theta3)*cos(theta4)+L4*cos(theta1)*sin(theta2)*sin(theta4), L4*sin(theta1)*cos(theta2)*cos(theta3)*cos(theta4)+L4*cos(theta1)*sin(theta3)*cos(theta4)+L4*sin(theta1)*sin(theta2)*sin(theta4), L2+L3*cos(theta2)*sin(theta3)+L4*sin(theta2)*sin(theta4)];
    P5 = P4 + [L5*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)-L5*sin(theta1)*sin(theta3)*cos(theta4)*cos(theta5)+L5*cos(theta1)*sin(theta2)*sin(theta4)*cos(theta5)-L5*cos(theta1)*cos(theta2)*sin(theta3)*sin(theta5), L5*sin(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)+L5*cos(theta1)*sin(theta3)*cos(theta4)*cos(theta5)+L5*sin(theta1)*sin(theta2)*sin(theta4)*cos(theta5)-L5*cos(theta2)*sin(theta3)*sin(theta5), L2+L3*cos(theta2)*sin(theta3)+L4*sin(theta2)*sin(theta4)+L5*cos(theta3)*sin(theta5)];
    P6 = P5 + [L6*cos(theta1)*cos(theta2)*cos(theta3)*cos(theta4)*cos(theta5)*sin(theta6)-L6*sin(theta1)*sin(theta3)*cos(theta4)*cos(theta5)*sin(theta6)+L6*cos(theta1)*sin(theta2)*sin(theta4